AN
INTELLIGENT
APPROACH
FOR
MULTI-RESPONSE
OPTIMIZATION:
A
CASE STUDY OF NON-TRADITIONAL
MACHINING PROCESS
June
2012
Jambeswar Sahu
Department of Mechanical Engineering
National Institute of Technology
AN INTELLIGENT APPROACH FOR MULTI-RESPONSE
OPTIMIZATION: A CASE STUDY OF NON-TRADITIONAL
MACHINING PROCESS
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF TECHNOLOGY
IN
PRODUCTION ENGINEERING
[MECHANICAL ENGINEERING]
ByJAMBESWAR SAHU
210ME2245
Under the supervision of
Prof. S.S.MAHAPATRA
DEPARTMENT OF MECHANICAL ENGINEERING
NATIONAL INSTITUTE OF TECHNOLOGY, ROURKELA
Dedicated to my parents & Guide
NATIONAL INSTITUTE OF TECHNOLOGY
ROURKELA-769008
CERTIFICATE
This is to certify that the thesis entitled “AN INTELLIGENT
APPROACH FOR MULTI-RESPONSE OPTIMIZATION: A CASE
STUDY OF NON-ITRADITIONAL MACHINING PROCESS
”
which is
being submitted by JAMBESWAR SAHU as partial fullfilment of Master
of Technology degree in Production Engineering (Mechanical Engineering)
during the academic year 2010-2012 in the Department of Mechanical
Engineering, National Institute of Technology, Rourkela.
Date: Prof. Siba Sankar Mahapatra
Department of Mechanical Engineering National Institute of Technology
ACKNOWLEDGEMENT
Successful completion of work will never be one man’s task. It requires hard work in right direction. There are many who have helped to make my experience as a student a rewarding one. In particular, I express my gratitude and deep regards to my thesis supervisor Dr. S.S. Mahapatra, Department of Mechanical Engineering, NIT
Rourkela for kindly providing me to work under his supervision and guidance. I extend
my deep sense of indebtedness and gratitude to him first for his valuable guidance, inspiring discussions, constant encouragement & kind co-operation throughout period of work which has been instrumental in the success of thesis.
I extend my thanks to Dr. K.P. Maity, and Head, Dept. of Mechanical
Engineering for extending all possible help in carrying out the dissertation work directly
or indirectly.
I express my sincere gratitude to Dr. Saurav Datta, Kunal Nayak, Department of
Mechanical Engineering, NIT, Rourkela and other staff members for their indebted
help in carrying out experimental work and valuable suggestions. I am also thankful to all the staff members of the department of Mechanical Engineering, NIT Rourkela and to all my well-wishers for their inspiration and help.
I greatly appreciate & convey my heartfelt thanks to Shailesh Dewangan, Chinmaya Mohanty, Debaprasanna Puhan, Layatit Dev Das, dear ones & all those who helped me in completion of this work.
I feel pleased and privileged to fulfill my parent’s ambition and I am greatly indebted to them for bearing the inconvenience during my M Tech. course.
JAMBESWAR SAHU
DECLARATION
We hereby declare that the thesis entitled “AN INTELLIGENT APPROACH FOR MULTI-RESPONSE OPTIMIZATION: A CASE STUDY OF NONITRADITIONAL MACHINING PROCESS” is a bonafied record of work done by me, as a functional part towards the fulfillment of Master of Technology degree in Production Engineering specialization (Mechanical) from National Institute of Technology, Rourkela during the academic year 2010-2112.
This is purely academic in nature and it has not formed the basis, for the award of any Degree/ Diploma/Ascertain ship/ fellowship or similar title to any candidate.
iii
JAMBESWAR SAHU
iv
ABSTRACT
The present work proposes an intelligent approach to solve multi-response optimization problem in electrical discharge machining of AISI D2 using response surface methodology (RSM) combined with optimization techniques. Four process parameters (factors) such as discharge current (Ip), pulse-on-time (Ton), duty factor (τ) and flushing pressure (Fp) and four important responses like material removal rate (MRR), tool wear rate (TWR), surface roughness (Ra) and circularity (r1/r2) of machined component are considered in this study. A Box-Behnken RSM
design is used to collect experimental data and develop empirical models relating input parameters and responses. Genetic algorithm (GA), an efficient search technique, is used to obtain the optimal setting for desired responses. It is to be noted that there is no single optimal setting which will produce best performance satisfying all the responses. In industries, to solve such problems, managers frequently depend on their past experience and judgement. Human intervention causes uncertainties present in the decision making process gleaned into solution methodology resulting in inferior solutions. Fuzzy inference system has been a viable option to address multiple response problems considering uncertainties and impreciseness caused during judgement process and experimental data collection. However, choosing right kind of membership functions and development of fuzzy rule base happen to be cumbersome job for the managers. To address this issue, a methodology based on combined neuro-fuzzy system and particle swarm optimization (PSO) is adopted to optimize multiple responses simultaneously. To avoid the conflicting nature of responses, they are first converted to signal-to-noise (S/N) ratio and then normalized. The proposed neuro-fuzzy approach is used to convert the responses into a single equivalent response known as Multi-response Performance Characteristic Index (MPCI). The effect of parameters on MPCI values has been studied in detail and a process model has been developed. Finally, optimal parameter setting is obtained by particle swarm optimization technique. The optimal setting so generated that satisfy all the responses may not be the best one due to aggregation of responses into a single response during neuro-fuzzy stage. In this direction, a multi-objective optimization based on non-dominated sorting genetic algorithm (NSGA) has been adopted to optimize the responses such that a set of mutually dominant solutions are found over a wide range of machining parameters. The proposed optimal settings are validated using thermal-modeling of finite element analysis.
v
Contents
Description
Page No Certificate i Acknowledgement ii Declaration iii Abstract iv Contents… vList of figures vii
List of tables ix
Chapter 1 Background and motivation 1
Chapter 2 Literature Review 9
Chapter 3 Experimental details 18
Chapter 4 Optimization strategy
4.1 Introduction 34
4.2 Multi-response optimization using NEURO-FUZZY system 34
4.3 Optimization technique
4.3.1 Particle swarm optimization 39
4.3.2 Genetic algorithm 42
4.4 Multi-objective optimization using non dominated sorting genetic algorithm
NSGA 47
4.5 Conclusions 51
Chapter 5 Results and discussion 52
5.1 Introduction
5.2 Optimization of single response
5.2.1 Material Removal Rate 52
5.2.2 Tool wear rate 60
vi
5.2.4 Circularity 74
5.3 Multi-response optimization using neuro-fuzzy approach 85
5.4 Multi-response optimization using non dominated sorting genetic algorithm
(NSGA) 94
5.5 Comparison of responses using brass and copper tool 103
5.6 White layer thickness and crack analysis 104
5.7 Conclusions
Chapter 6 Thermo-Physical Modelling
6.1 Introduction 110
6.2 Thermal analysis of EDM 110
6.2.1 Assumption 111
6.2.2 Heat input, spark radius and boundary condition 111
6.2.3 Solution methodology 112
6.3 Result and comparison of model 113
6.4 Conclusions 116 Chapter 7 Conclusions 7.1 Introduction 117 7.2 Summery of findings 117 7.3 Limitation of study 119 7.4 Future scope 119 References 120 Publication Details 128
vii
LIST OF FIGURES
Figure Title Page No
1.1 Classification of non-traditional machining process 1
1.2 Principle of EDM process 2
1.3 Engraved plate sent by Alessandro Volta to Joseph Priestley, showing
the spark produced by short-circuit of a Leyden jar 4
1.4 Sketches of erosion craters on cathode surface, observed by Joseph
Priestley 4
3.1 Die Sinker EDM Model: PS 50ZNC 19
3.2 Brass Tool 21
3.3 Copper Tool 22
3.4 Electronic Balance weight machine 22
3.5 Talysurf 23
3.6 Microscope with camera attachment 24
3.7 Scanning Electron Microscope (SEM). 24
3.8 Feret’s diameter 32
4.1 Flow Chart for fuzzy c-mean clustering 37
4.2 Depiction of the velocity and position updates in Particle Swarm
Optimization 41
4.3 Flow chart of genetic algorithm 43
4.4 One site crossover operation 46
4.5 Two site crossover operation 46
4.6 Flow chart for NSGA algorithm 51
5.1 Normal plot of residuals for MRR using brass tool 56
5.2 Normal plot of residuals for MRR using copper tool 56
5.3 Surface plot for MRR using brass tool 57
5.4 Surface plot For MRR using brass tool 58
5.5 Surface plot for MRR using copper tool 59
5.6 Surface plot for MRR using copper tool 59
5.7 Normal plot of residuals for TWR using brass tool 63
5.8 Normal plot of residuals for TWR using copper tool 63
5.9 Surface plot For TWR using brass tool 64
5.10 Surface plot For TWR using brass tool 65
5.11 Surface plot for TWR using copper tool 66
viii
5.13 Normal probability of residuals for Ra using brass tool 70 5.14 Normal probability of residuals for Ra using copper tool 70
5.15 Surface plot for Ra using brass tool 71
5.16 Surface plot for Ra using brass tool 72
5.17 Surface plot for Ra using copper tool 73
5.18 Surface plot for Ra using copper tool 73
5.19 Normal probability plot of the residuals for circularity using brass tool 77 5.20 Normal probability plot of the residuals for circularity using copper tool 77
5.21 Surface plot for circularity using brass tool 79
5.22 Surface plot for circularity using brass tool 79
5.23 Surface plot for circularity using copper tool 80
5.24 Surface plot for circularity using copper tool 80
5.25 The convergence curve for MRR using brass and copper tool
respectively 81
5.26 The convergence curve for TWR using brass and copper tool
respectively 83
5.27 The convergence curve for Ra using brass and copper tool respectively 84 5.28 The convergence curve for circularity using brass and copper tool
respectively 84
5.29 Training in neural network 88
5.30 Regression plot for training data 5.31 Regression plot for testing data
5.32 Membership function plot 91
5.33 Surface plot of MPCI vs Ip, Ton 93
5.34 Surface plot of MPCI vs Ip, τ 93
5.35 The convergence curve 94
5.36 Pareto-optimal front for objectives MRR and TWR 98
5.37 Pareto-optimal front for objectives Ra and Circularity 98
5.38 Pareto-optimal front for objectives MRR and TWR 102
5.39 Pareto-optimal front for objectives Ra and Circularity 102
5.40-47 White layer thick ness 104-108
5.48-49 SEM picture of machined surface 109
6.1 Two-dimensional axisymmetric model 111
6.2 Mode of heat transfer in the work piece 111
6.3 Temperature distribution 114
6.4 Predicted bowl shaped crater using the FEM analysis 114
ix
List of Tables
Table No Title
Page No
2.1 Summary of publications referred 9
3.1 Specification of PS 50ZNC 19
3.2 Properties of AISI D2 steel 20
3.3 Roughness measuring conditions 23
3.4 Process parameters in EDM 25
3.5 Factors and their levels 26
3.6 Experimental plan for Box-Behnken design 28
3.7 Experiment table for brass AISI D 2 steel combination 29 3.8 Experiment table for copper AISI D 2 steel combination 30
3.9 Response table using brass tool 32
3.10 Response table using copper tool 33
5.1 MRR using Brass and Copper tool 53
5.2 ANOVA for MRR using Brass Tool 54
5.3 ANOVA for MRR using copper Tool 55
5.4 Tool wear rate of brass and copper tool 60
5.5 ANOVA for brass tool wear rate 61
5.6 ANOVA for copper tool wear rate 62
5.7 Ra using Brass and Copper tool 67
5.8 ANOVA for Surface Roughness (Ra) using brass tool 68
5.9 ANOVA for Surface Roughness (Ra) using copper tool 69
5.10 Circularity using Brass and Copper tool 74
5.11 ANOVA for Circularity using brass tool 75
5.12 ANOVA for Circularity using copper tool 76
5.13 Optimal condition and optimal value 82
5.14 Signal-to-noise ratio and Normalized value 86
5.15 Membership values from FCM 87
5.16 Adjusted membership value 89
5.17 MPCI 91
5.18 ANOVA for MPCI 92
5.19 Pareto Optimal solution set and corresponding variable settings 95-97 5.20 Pareto Optimal solution set and corresponding variable settings 99-101 5.21 Optimal solution for individual responses and corresponding
variable 103
5.22 Condition for optimal EDM performance using neuro-fuzzy model 103
x
6.1 Process parameter for ANSYS 113
6.2 Comparison of AI and thermo-physical model 116
7.1 Optimal condition and optimal value 117
7.2 Condition for optimal EDM performance using neuro-fuzzy model 118
1
Chapter 1
BACKGROUND AND MOTIVATION
1.1. Introduction
The world is advancing technically in the field of space research, missile and nuclear industry. These industries demand very complicated and precise components having some special requirements. The challenges are taken by the new development taking place in manufacturing field. Now-a-days, many new materials and non-traditional machining and forming methods have been evolved to process difficult-to-machine materials, which are being put to commercial use with time. The non-traditional methods of machining have several advantages over traditional method of machining. Non-traditional methods are not limited by hardness, toughness, and brittleness of materials and can produce any intricate shape on any work piece material by suitable control over various process parameters. Non-traditional machining process can be classified into various groups depending on type of energy required, mechanism of material removal, source of energy required, and medium of energy transfer as described in Figure 1.1. [1].
Energy required
Non-traditional machining
Material removal mechanism Source of energy required Medium of energy trasnfer
Mechanical Thermal & Electrothermal Erosion Chemical & Electrochemical Hydrostatic pressure Ionoc dissolution Vapourization Hot gases High current density
Electron electrolyte High velocity particles Ionised material Ionised material USM WJM AWJM IJM EDM EBM LBM PAM IBM ECM ECG ECH ECD
2
1.2. Electric discharge machining
Electrical Discharge Machining (EDM) is a non-traditional machining process used for machining any toughened and high strength to weight ratio conductive materials which are hard enough to cut by traditional processes (for example hardened steel, tungsten carbide, special alloys for aerospace applications). Furthermore, any complex cutting geometry, sharp angles and internal corners having surface state roughness less than 100 µm and precise machining (<1µm) can be produced. Therefore, EDM process and AISI D2 steel have extensively used in manufacturing industries, especially aerospace, ordnance, automobile, electronics, domestic appliances, packaging, telecommunication, surgical instruments and general engineering [2,3,4]. On the other hand, low material removal rate (order of 100 mm3/min), surface modification of the machined work piece (white layer and heat affected zone) and limited size of work piece and tool have a disadvantage towards EDM process.
1.2.1. Principle
The material removal mechanism is owing to controlled erosion through a series of electric sparks between the tool and the work piece. The thermal energy of the sparks leads to intense heat conditions on the work piece causing melting and vaporizing of work piece material. The sparks are created in a dielectric liquid may be water or oil. There is no mechanical contact between tool and work piece during the whole process but in machining process small volumes of work piece material successively removed by melting or vaporized during a discharge. A simple explanation of erosion process as a result of single discharge is shown in Figure 1.2.
(a) Pre-breakdown: voltage applied between
the Electrode and the workpiece
(b) Breakdown : dielectric breakdown, creation of the plasma
channel
(c) Discharge : heating, melting and
vaporizing of the workpiece material
(d) End of the discharge : plasma implosion,
removing of the molten metal pool
(e) Post-discharge : solidifying and flushing
of the eroded particles by the dielectric Figure 1.2. Principle of EDM process
Initially, voltage is applied between tool and work piece. The dielectric break down is initiated, while tool moves towards work piece and gap voltage increases till sufficient breakdown occurs. The break down location is the closest point between the electrodes [5]. As
3
breakdown occurs voltage falls and a current rises sharply. The dielectric has been ionised and plasma channel has been created between electrodes. The current is then maintained for continuous bombardment of ions and electrons on the electrodes, which leads to a huge amount heat generation and creates a molten metal pool (of both work piece and tool) at the surface. There may be possibility that, a small amount of metal can be directly vaporised due to huge amount heat generation. As the plasma channel expands with time, the radius of molten metal pool is also increases. During the discharge, maintaining inter electrode gap (IEG) is a difficult task as IEG increases with discharge current. Therefore an automatic positioning system (APOS) and sensitivity (SEN) is employed for maintaining the IEG. After the discharge current and voltage are shut down during Toff time and the molten pool is carried out by flushing leaving a tiny crater in the work piece.
1.2.2. History
The history of electric discharge machining describes from the discovery of electric discharge. In the first half of the 18th century investigation of electrostatic phenomena were performed with frictional machines. Then the around 1745, first sparks and pulsed arcs were produced with “Leyden jars”, an early form of capacitor invented in Germany and in the Netherlands [6] (Figure 1.3). Powerful discharges were created by putting several Leyden jars in parallel, creating thus a “battery”.
Joseph Priestley (1733-1804), an English theologian and chemist, was the first to discover erosion craters left by electric discharges on the cathode surface in 1766:
“June the 13th, 1766. After discharging a battery, of about forty square feet, with a smooth brass knob, I accidentally observed upon it a pretty large circular spot, the center of which seemed to be superficially melted. (...) After an interruption of melted places, there was an intrie and exact circle of shining dots, consisting of places superficially melted, like those at the center.” (Figure 1.4)
“June the 14th, 1766. (...) Examining the spots with a microscope, both the shining dots that formed the central spot, and those which formed the external circle, appeared evidently to consist of cavities, resembling those on the moon, as they appear through a telescope, the edges projecting shadows into them, when they were held in the sun” [7].
4
Figure 1.3. Engraved plate sent by Alessandro Volta to Joseph Priestley, showing the spark produced by short-circuit of a Leyden jar (1775) [8];
Figure 1.4. Sketches of erosion craters on cathode surface, observed by Joseph Priestley in 1766 [7].
Priestley used pulsed and oscillating discharge to investigate the influence of electrode material on the crater size. In 1799 Alessandro Volta (1745-1827) was invented that continuous discharges can be produced with battery of electrochemical cells. In 1802, Vasilii Petrov at St-Petersburg first to produce continuous carbon arc by developing very large voltaic batteries [9]. Humphry Davy (1778-1829) was discovered arcs, but his discovery remained ignored and forgotten for over a century. Petrov‟s in the Royal Institution of London around 1808, re-discovered independently carbon arcs using the huge voltaic battery.
5
The principle of EDM was invented by Russian scientists Boris and Natalya Lazarenko in Moscow in 1943, while they are assigned to Soviet government to investigate the wear caused by sparking between tungsten electrical contacts that was a problem for maintenance of automotive engines. Putting the electrodes in oil, they found that the sparks were more uniform than in air. Then they reverse the phenomenon, and to use controlled sparking as an erosion method [10]. Lazarenkos developed the first EDM machines during world war, which were very useful to erode hard metals like tungsten or tungsten carbide. The „Lazarenko circuit‟ remained the standard EDM generator for years. In the 1950‟s, by understanding the erosion phenomenon, Swiss industries produced the first EDM machines [11-13].
1.2.3. State-of-the-art
Sixty-two year after the first industrial machine, EDM has made significant progress. Recently improvements in accuracy of machined parts, speed of machining and surface roughness is achieved by adopting automation, process control, changing dielectric, flushing and generator design [14-17]. Though EDM have the ability such as machining hard material and complex geometry, this process has to improve constantly in order to stay competitive and economically interesting in the modern tooling market against other traditional or new machining technique [16-18].
These limitations offer new opportunities for EDM development and growth as follows:
There is a need to develop screening methodologies for EDM process for a high strength to weight ratio material (AISI D2 steel) machined by copper and brass tool.
A much better understanding is needed for the basic physics and chemistry of EDM processes that capture the complexity part production.
Technical and operation related advances are needed to ensure that EDM processes are more reliable and predictable than other non-traditional manufacturing processes.
Control algorithms based on predictive models of system response to process changes are needed to maximize the performance of EDM machines.
Developments of formalized standards for the EDM industry will help to achieve continued growth and further advancements of EDM technologies.
6
1.3. Research objectives
To sustain in this competitive market, product has to be modified and new product has to be developed. There are many external things which impose for development or modification. Among these materials, technologies, services and the attention paid to the end user requirements are significant. Though technological barriers exist, as in most technology areas, it is important to overcome them by developing proper understanding of process with related attributes. In this direction, next chapter (Chapter 2) explains the various efforts directed for improving the industrial feasibility of EDM process. Exhaustive literature review reveals that, there are many work carried out in EDM, but less work carried out using brass as tool material. The work represents choosing the best tool among two and a suitable condition for improving EDM performance. In this direction, present work emphasise on the EDM process functionality to understand the multiple interacting phenomena involved with this process and make it more reliable and predictable than other non-traditional manufacturing processes.
Based on these guiding principles, the objective of present research are as follows:
Study on effect of process parameters on EDM performance. EDM performance is measured in terms of material removal rate, tool wear rate, surface roughness and circularity.
Analysis of experimental results using statistical methods.
Determination of relationship between process parameters and properties studied. Neuro-fuzzy approach for solving multi-response problem.
Optimum parameters selection for overall improvement in EDM performance using genetic algorithm and particle swarm optimization.
Non-dominated sorting genetic algorithm (NSGA) to obtain pareto optimal setting. Theoretical validation of material removal rate and tool wear rate model by thermal
modeling using finite element analysis.
Methodology adopted for achieving these objectives are quite general and can provide common methods for measuring the benefits and limitations of various RP processes.
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1.4. Thesis outline
The remainder of this thesis is organized as follows: Chapter 2: Literature review
Includes a literature review to provide a summary of the base of knowledge already available involving the issues of interest.
Chapter 3: Experimental details
Include a description of the setup, material, sample preparation, measurement, design of experiments methodology and observation.
Chapter 4: Optimization stratergy
Describes the methodology and algorithm for multi-response optimization using neuro-fuzzy approach, optimization technique such as genetic algorithm, particle swarm optimization, and multi-objective optimization using non-dominated sorting genetic algorithm.
Chapter 5: Results and discussions
The effects of process parameters on responses are discussed. The relation between process parameter with responses are established by regression equation and optimized by genetic algorithm. Neuro-fuzzy method is proposed to covert multi-responses into an equivalent single response and optimum process conditions are determined for overall improvement of EDM performance using particle swarm optimization technique. The single optimal solution may change according to the requirement and also setting may not be available in machine, therefore non-dominated sorting genetic algorithm (NSGA) is proposed to obtain a set of pareto optimal solution to improve decision makers space.
Chapter 6: Theoretical validation of MRR and TWR
The optimal setting may not available in machine. Therefore to check validation of model, thermal modeling has been carried out using ANSYS software.
Chapter 8: Executive summary and conclusions
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1.5. Conclusions
Present chapter highlights the importance of EDM in manufacturing industry, history of EDM and objective of work. The general attributes of EDM can be put together as:
Any conductive material can be machined irrespective of hardness. Able to build complex 3D geometries including enclosed cavities. Process is automatic and based tool design.
Require minimal or no human intervention to operate.
These characteristics open new opportunities for faster product development in a simplified, minimal time, better performance and cost effective way. To improve the EDM performance in particular, research objective together with work outline is presented in this chapter.
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Chapter 2
LITERATURE SURVEY
2.1. Introduction
One of the current challenges faced by manufacturing industries is the reduction of process time and improvement of performance through optimization of controllable process parameter using different optimization technique. This can be obtained by experimentation or using any model developed from experiment. Although performance improvement in EDM has been studied extensively, proper selection of machining parameters for the best process performance is still a challenging job. In this direction, the current chapter highlights some research paper on EDM describing the effect of process parameters on EDM performance like material removal rate (MRR), tool wear rate (TWR), surface roughness (Ra), white layer thickness, surface cracks, etc. Literature survey begins with papers published after 1995 with maximum attention paid to last ten years. The search was restricted on those articles for which full text was available. Table 2.1 provides the source and number of citations from each source.
Table 2.1. Summary of publications referred
Source Citation
Applied Mathematical Modelling 1
Applied Soft Computing 1
Computational Material Science 1
European Journal of Operational Research 1
IEEE Transaction on Evolutionary Computation 2
IEEE Transaction on Plasma Science 2
International Journal of Advanced Manufacturing Technology 8
International Journal of Engineering and Technology 1
International Journal of Integrated Engineering. 1
International Journal of Machine Tools and Manufacture 13
Journal of Applied Physics 3
Journal of Decision and Mathematical Sciences 1
Journal of Materials Processing Technology 18
Journal of Engineering for Industry 2
Journal of Manufacturing Processes 1
Journal of Engineering Research and Studies 1
10
Journal of Reinforced Plastics and Composites 1
Mathematical and Computer Modelling 1
Materials and Manufacturing Processes 3
Material Science and Applications 1
Proceedings of Institution of Mechanical Engineering Journal of Engineering
Manufacture 1
Proceedings of the 11th International Symposium for Electro Machining 1 Proceedings of the 12th International Symposium for Electro Machining 2
Quality and Reliability Engineering 2
Soviet Physics-Technical Physics 1
The Arabian Journal for Science and Engineering Science 1
Total Quality Management 1
World Academy of Science, Engineering and Technology 1
World Congress on Computer Science and Information Engineering 1
http://www.lindquiststeels.com/documentation/d2.pdf 1
http://cadm.zut.edu.pl/pub/prawie%20wszystko%20o%20edm%20(ang).pdf 1
Books 10
Total 87
The papers are broadly classified into five categories, such as theoretical model of EDM, numerical model of EDM, statistical model of EDM, soft computing model of EDM and technological modification of basic EDM process.
2.2. Theoretical model of EDM
Singh and Ghosh considered that melting is the main process for metal removal. For short pulse (< 5µs), melting does not accounted as metal does not get enough time to get adequately heated and almost no melting takes place. The electrostatic force acting on the surface is a very important factor in the removal of metal for short pulses. For long pulses (discharge duration > 100µs), this electrostatic force becomes very small and does not play a significant role in the removal of metal. In the model proposed, the electro- static force acting on the metal surface and the stress distribution inside the metal due to this electrostatic force have been estimated. The variation of the yield strength with depth inside the metal has also been found out and finally the „crater depth‟ due to this electrostatic force has been calculated. The model also predicts that for, short pulses the crater depth is proportional to square root of current. The same result is also found by the experiments of Williams [19, 20]. Marafona and Wykes investigated the optimisation of the process which uses the effect of carbon, which has migrated from the
11
dielectric to tungsten–copper electrodes. This work has led to the development of a two-stage EDM machining process where different EDM settings are used for the two stages of the process giving a significantly improved material removal rate for a given tool wear ratio. It is observed that, a black layer modified surface is produced on the tool in the first stage which inhibits tool wear, thus giving better tool wear for a given material removal rate in the second stage. The responses MRR, TWR, Ra are taken as EDM performance and conclude that the percentage of carbon in the „black‟ layer is very important in the improvement of the EDM performance [21]. Chen and Mahdivian proposed a theoretical model to estimate the material removal rate and surface quality. The model provides equations to calculate work piece MRR and maximum peak-to-valley height is used for surface finish. Process parameters such as discharge current, pulse duration time and interval time at different level wear taken to conduct experiment and their effect on MRR and surface roughness were studied. It is observed that the theoretical model and experimental results are identical [22]. A finite element model has been developed to estimate the temperature field and thermal stresses in HSS due to Gaussian distributed heat flux of a spark during EDM. First, the developed code calculates the temperature in the work piece and then the thermal stress field is estimated using this temperature field. The effects of process variables (current and duty cycle) on temperature distribution and thermal stress distribution have been reported. The damaging nature of the thermal stresses as they develop during EDM is illuminated. It is observed that, after one spark, substantial compressive and tensile stresses develop in a thin layer around the spark location. It is also found that the thermal stresses exceed the yield strength of the work piece mostly in an extremely thin zone near the spark [23]. Thermo-physical model using finite element analysis and joule heating factor is developed by Marafona and Chousal to obtain the material removal from anode electrode, cathode electrode and maximum roughness at cathode surface. The theoretical results are compared with experimental results. It is observed that the anode material removal efficiency is smaller than that of cathode because there is a high amount of energy going to the anode and also a fast cooling of this material. A comparison is made 2D and 3D finite element analysis and observed that 2D axisymmetric finite element has an easier formulation than the 3D finite element and allows a reduction in the CPU time with very similar results. The difference between both axisymmetric and 3D was found around 100 times, i.e. 3D modelling has taking1180 s while the 2D only 14.5 s [24]. Recently, a new approach is proposed by Mahardika et al. to determine machining by
12
EDM processes using the product of the thermal conductivity (λ), melting point (θ) and electrical resistivity (ρ) of the work piece in relation to the machining time. Earlier developed theory was the function of thermal conductivity (λ) and melting point (θ). It is observed that the recent theory gives better result than previous one [25].
2.3. Numerical model of EDM
Das et al. developed an EDM simulation model using finite element for calculation of deformation, microstructure and residual stresses. The process parameters such as power input, pulse duration, etc. are used to predict the transient temperature distribution, liquid- and solid-state material transformation, and residual stresses that are induced in the work piece as a result of a single-pulse discharge. The model developed by DEFORM software has been validated using experimental data [26]. The measured and simulated crater morphology of EDM using ANSYS is compared for single discharge and a sequence of discharges. The thermal channel base parameters are computed along with measured current and voltage curves [27]. An axisymmetric two-dimensional model for powder mixed electric discharge machining (PMEDM) has been developed using the finite element method (FEM) in ANSYS (version 5.4) software. Some aspects such as temperature- sensitive material properties, shape and size of heat source, percentage distribution of heat among tool, work piece and dielectric fluid, pulse on/off time, material ejection efficiency and phase change (enthalpy) are used in the model to predict the thermal behaviour and material removal mechanism. The effect of various process parameters on temperature distributions along the radius and depth of the work piece are studied. Finally, the model has been validated by comparing the theoretical MRR with the experimental data [28]. Joshi and Pande developed an intelligent technique using ANSYS to study the effect of current, spark on time, discharge voltage, duty factor on MRR, TWR, crater-depth and crater,-height. A neural-network-based process model is proposed to establish the relation input process and process response and to optimize the process parameters for better performance [29]. In 2010 Joshi and Pande developed an axisymmetric two-dimensional model using ANSYS to study the effect of of process parameter such as discharge current, discharge duration, discharge voltage and duty cycle on the process performance. Experimental studies were carried out to study the MRR and crater shapes produced during actual machining. When compared with the reported analytical models, ANSYS model was found to predict results closer to the experimental results
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[30]. Pradhan used ANSYS 12.0 to develop an axisymmetric two-dimensional model for electric discharge machining AISI d2 steel. It is observed that the compressive thermal stresses are developed beneath the crater and become tensile as we move away from the axis of symmetry. The radial component of the residual stresses reaches its maximum values close to the surface but diminishes very rapidly to comparatively low values of compressive residual stresses. It is found that the radial component of the residual stresses acquired from FEM are dominant than other components for all the machining parameter combinations [30].
2.4. Statistical model of EDM
Habib has analyzed the effect of machining parameters such as pulse current, gap voltage and pulse-on-time on MRR and TWR in EDM using response surface methodology. It is observed how MRR and TWR increase with increasing values of process parameters [32]. Chattopadhyay et al. have used Taguchi‟s design of experiment (DOE) approach to conduct experiment on rotary EDM using EN8 steel and copper as work piece-tool combination and developed empirical relations between performance characteristics (MRR and EWR) and process parameters such as peak current, pulse-on-time and rotational speed of tool electrode. It is found that peak current and rotational speed of tool electrode influence significantly on both the responses [33]. DOE approaches have been extensively used to determine best machining parameters in EDM. The DOE approaches are well suited to obtain optimal parametric combination for a single response problem. The method breaks down when multiple responses are simultaneously optimized due to some technical and practical reasons [34]. The influence of gap voltage, discharge current, pulse duration, pulse interval, flushing pressure on material removal rate, tool wear rate and surface roughness of EDM process using tungsten carbide (WC) as work piece and copper tungsten as electrode (CuW). It is observed that WC is suitable for EDM tool material and there exist an optimal condition for precision machining of WC although the condition may vary with composition of material [35]. Tebin et al. conducted the experiment on EDM to study the effect of discharge current, the pulse-on duration, the pulse-off duration, the tool electrode gap, and the tool material on MRR and TWR using steel 50CrV4 as work piece, copper and graphite as tool [36]. Pradhan and Biswas have adopted RSM design to conduct experiment on EDM and investigated the effect of four controllable input variables viz., discharge current, pulse duration, pulse-off-time and voltage on machining performance using
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AISI D2 steel and copper as work piece-tool combination. It is observed that discharge current and pulse-on-time have significant effect on surface roughness [37]. Helmi et al. have investigated surface roughness and material removal rate in electro discharge grinding process employing Taguchi method when tool steel is machined with brass and copper electrodes. It is observed from analysis of variance that peak current and pulse-on-time are the significant factors influencing the performance characteristics [38]. Yunus analyzed the effect of factors such as pulse current, pulse-on-time, pulse-off-time, and voltage on surface roughness of machined component using factorial experiments and suggested optimal parameter setting to minimize surface roughness [39]. Prabhu and Vinayagam have experimentally demonstrated that surface roughness and micro-cracks on work piece (AISI D2 tool steel) can be substantially reduced if the tool (electrode) is coated with a carbon nono-tube layer [40]. Metal removal process in EDM is characterized by nonlinear, stochastic and time varying characteristics. In EDM, a quantitative relationship between the operating parameters and controllable input variables is often required. Many regression techniques have been used for modelling the EDM process [41].
Neural networks and fuzzy systems form an alternative approach to generalize the experimental results and develop the system model accurately. Unlike milling and drilling operations, operating speeds in EDM are very low. Large electric current discharge can enhance speeds but reduces the dimensional quality of machined surface. Similarly, the material removal rate is also affected by other process parameters. These parameters are selected from standard tables or by experience to improve the output performance of the process. Even in the computer controlled environments involving online process control, this selection is not an easy task. Presently many optimization techniques are being used in EDM practice to obtain the best process parameters. Kansal et al. adopted the response surface optimization scheme to select the parameters in powder mixed EDM process [42]. The next year Keskin et al. used design of experiments (DOE) for the determination of the best machining parameters in EDM [43].
The approaches based on DOE are well suited to obtain optimal parametric combination for a single response problem. The methods break down when multiple responses are simultaneously optimized due to some technical and practical reasons. In this direction, Su and Tong indicated that Taguchi method can satisfactorily address a single response problem. However, they proposed that principal component analysis can be combined with Taguchi method to optimize the multi-response production process [44]. Tong et al. proposed a methodology that combines
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principal component analysis with TOPSIS method to convert multiple responses into a single equivalent response. The reason of applying PCA is to obtain uncorrelated principal components when PCA is applied to responses. Finally, closeness coefficient obtained through TOPSIS is treated as single response [45]. Tong and Su proposed a fuzzy TOPSIS method to convert multi-responses (deposition thickness and refractive index) in plasma enhanced chemical vapor deposition (PECVD) process into single response. The relative closeness coefficient is regarded as a performance measurement index to find the optimal combination of eight controllable factors [46]. Tarng et al. have used fuzzy logic in Taguchi method for simultaneous optimization of multiple responses in a submerged arc welding process. The process parameters viz., arc current, arc voltage, welding speed, electrode protrusion, and preheat temperature are optimized with considerations of the responses such as deposition rate and dilution. The optimal setting suggested by Taguchi method is tested through few confirmatory tests [47]. To solve this type of multi-optimization problem in EDM, Lin et al. used grey relation analysis based on an orthogonal array and fuzzy based Taguchi method [48, 49, 50].
2.5. Soft computing model of EDM
Researchers, of late, are focusing upon employment of artificial intelligence (AI) techniques viz. ANN, GA, fuzzy logic, etc. for the process modelling and optimization of manufacturing processes which are expected to overcome some of the limitations of conventional process modelling techniques. Genetic algorithm (GA) with artificial neural network (ANN) is used to find out optimal process parameters for improving performances in EDM process using graphite as tool and nickel based alloy as work piece [51]. A similar approach has been considered by Su et al. from the rough cutting to the finish cutting stage. In most of the studies, multiple objectives are transformed into a single objective and attempts to find optimal parameters [52]. However, non-dominated sorting genetic algorithm (NSGA) is used to optimize machining parameters in WEDM considering surface roughness and cutting speed as the output parameters. Multiple linear regression models have been developed to represent the relation between inputs and outputs [53]. Mandal et al. used neural networks to predict the MRR and Ra trained by experimental data from EDM of SiC and multiple response problem is solved using NSGA-II by getting pareto-optimal solution [54]. In order to overcome the single response optimization problem of Taguchi method, Liao proposed an effective procedure called PCR-TOPSIS that is
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based on process capability ratio (PCR) theory and on the theory of order preference by similarity to the ideal solution (TOPSIS) to optimize multi-response problems [55]. Two case studies performed by Tarang et al. [56] and Reddy et al. [57] were resolved using the proposed method and the result shows that PCR-TOPSIS can yield a good solution for multi-response problems.
Antony et al. have used Taguchi design and proposed a neuro-fuzzy system for simultaneous optimization of multiple responses [58]. A back propagation neural network (BPNN) with Levenberg-Marquardt (LM) algorithm have proposed by Panda and Bhoi [59] for the prediction of MRR. Recently, simulated annealing (SA) technique with ANN approach has been used for optimization of MRR and surface roughness [60]. The material removal rate has been optimized in micro-EDM usingartificial neural network and genetic algorithms [61].
Particle swarm optimization (PSO) is a computational simulation technique based on the movement of organisms such as flocks of birds and schools of fish used to solve optimization problems. It has a population of search points to probe the search space where each individual is referred as a „particle‟ and represents a potential solution. These are associated with the best solution (fitness) it has achieved so far known as personal best (pbest) and overall best value and its location obtained so far by any particle in the population. This location is global best (gbest). Each particle moves its position in search domain and updates its velocity according to its own flying experience toward its pbest and gbest locations [62]. Neural network and non-dominating sorting genetic algorithm (NSGA II) is used to optimize the surface roughness and material removal rate of electro discharge machining of SiC parameters simultaneously. The effect of discharge current (Ip), pulse on time (Ton), pulse off time (Toff) on MRR and surface roughness were studied [63]. A multiple regression model is used to represent relationship between input and output variables of Wire-EDM process and a multi-objective optimization method based on a non-dominated sorting genetic algorithm (NSGA) is used to optimize machining performance such as cutting velocity and surface finish [64].
2.6. Technological modification of basic EDM
Many researchers have been carried out by modifying EDM process, changing dielectric or modifying dielectric medium. A silicon powder mixed electrical discharge machining experiment has been carried out and response surface methodology is used to plan the
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experiment. The effect of process parameters such as pulse-on-time, discharge current, duty cycle and concentration of the silicon powder on material removal rate and surface roughness are analyzed. It is observed that MRR is increasing with concentration of silicon powder and discernible improvement in surface roughness is observed with suspended silicon powder [65]. An ultrasonic assisted dry machining experiment has been conducted with powder additives. It is observed that EDM with powder additives is concerning more on increasing surface quality and material removal rate [66]. Aluminium powder mixed electric discharge machining of hastelloy material is conducted to analyze the effect of machining parameter such as discharge current, gap voltage, pulse-on-time and duty cycle on material removal rate, tool wear rate and surface roughness. It is observed that all process parameter have strong influence on MRR, TWR, wear ratio and surface roughness [67].
2.7. Conclusions
This chapter provide the insight into basic EDM process, technologically modified EDM process, different modelling technique, some optimization technique to optimize EDM performance and some soft computing techniques. The next chapter describes the experimental details in this study.
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Chapter 3
EXPERIMENTAL DETAILS
3.1. Introduction
EDM has significant advantages in terms of machining high strength to weight ratio material, high strength to volume ratio material, the flexibility and the possibility of producing very complex parts and shapes. One of the current challenges faced by EDM users is the improvement of quality and productivity of parts produced, which is allied with the accurate application of the specified performance. This makes it essential to understand the performance of EDM process with the variation of process parameters so make them reliable for industrial applications. To achieve this, the present chapter describes the materials and methods used for the testing of EDM process under investigation. It presents the details of material property, sample preparation, measurements. Material removal rate (MRR), tool wear rate (TWR), surface roughness (Ra) and circularity characteristics are considered as measure of process quality and productivity in accordance to industrial requirements. The methodology related to the design of experiment technique based on response surface method (RSM) is presented in this part of the thesis.
3.2. Set up
Experiments are carried out in a die sinking EDM machine (ELECTRONICA- ELECTRAPULS PS 50ZNC) shown in Figure 3.1 with servo-head (constant gap). The specification of machine is given in Table 3.1. Commercial grade EDM oil (specific gravity= 0.763, freezing point= 94°C) was used as dielectric fluid. Positive polarity for electrode and side flushing was used to conduct the experiments.
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Figure 3.1. Die Sinker EDM Model: PS 50ZNC
Table 3.1. Specification of PS 50ZNC
Mechanism of process Controlled erosion (melting and evaporation) through a series of electric spark
Spark gap 0.010- 0.500 mm
Spark frequency 200 – 500 kHz
Peak voltage across the gap 30- 250 V Metal removal rate (max.) 5000 mm3/min Specific power consumption 2-10 W/mm3/min
Dielectric fluid EDM oil, Kerosene, liquid paraffin, silicon oil, deionized water etc.
Tool material Copper, Brass, graphite, Ag-W alloys, Cu-W alloys . Materials that can be machined All conducting metals and alloys.
Shapes Microholes, narrow slots, blind cavities
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3.3. Work piece material
Steel is the common name for a large family of iron alloys. Steels can either be cast directly to shape, or into ingots which are reheated and hot worked into a wrought shape by forging, extrusion, rolling, or other processes. Wrought steels are the most common engineering material used, and come in a variety of forms with different finishes and properties. Tool steels typically have excess carbides (carbon alloys) which make them hard and wear-resistant. Most tool steels are used in a heat-treated state, generally hardened and tempered. The material used as work piece for electrical discharge machining is AISI D2 steel, which is basically an air-hardened high carbon, high chromium tool steel alloyed with molybdenum and vanadium characterized by:
High wear resistance High compressive strength
Good through-hardening properties High stability in hardening
Good resistance to tempering-back Moderate toughness (shock-resistance) Composition
It is composed of (in weight percentage) 1.55% Carbon (C), 0.60% Manganese (Mn), 0.60% Silicon (Si), 11.8% Chromium (Cr), 0.30% Nickel (Ni), 0.8% Molybdenum (Mo), 0.8% Vanadium (V), 1.00% Cobalt (Co), 0.25% Copper (Cu), 0.03% Phosphorus (P), 0.03% Sulphur (S), and the base metal Iron (Fe). Other designations of AISI D2 tool steel include UNS T30402. Table 3.2 list the properties of commercially available AISI D2 steel.
Table 3.2. Properties of AISI D2 steel
Property Value Unit
Density 7700 kg/m3
Mechanical property
Hardness Rockwell R 57 HRC
Tensile Strength 1736 MPa
Modulus of elasticity 200 GPa
Poissions ratio 0.29
Thermal properties
Thermal Conductivity 20 W/m-K
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Machinability
AISI D2 steel has a machinability rating 65, as compared with a rating of 100 for a 1% carbon tool steel [68]. Since AISI D2 steel has conductive in nature it is also suitable for electrical discharge machining process.
Application
Manufacturing sectors especially industries • Aerospace • Ordnance • Automobile • General engineering • Die making • Tool material 3.4. Sample preparation
The material, AISI D2 steel has brought in the form of bar of 85 mm diameter and 300 mm length. This is cut into round plates of size 85 mm diameter and 6 mm thickness, that suitable for machining. Then the sample is grind and properly cleaned to get flat surface.
3.5. Tool preparation
Since a large amount of heat is dealt in EDM owing to spark, the tool should be of a good conductive material with high melting point. Therefore, pure brass and pure copper are taken as the tool material having density 8400 kg/m3 and 8940 kg/m3 respectively. Two stepped tool of 25 mm machining diameter and 10 mm shank is made from a 25 mm diameter bar.
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Figure 3.3. Copper Tool
3.6. Measurements
3.6.1.Weighing machine
The weight of work piece and tool has taken by high precision balance Figure 3.4. This machine capacity is 300 gram and accuracy is 0.001 gram and Brand: SHINKO DENSHI Co. LTD, JAPAN, and Model: DJ 300S.
Figure 3.4. Electronic Balance weight machine 3.6.2.Talysurf
Surface roughness measurement was carried out using a portable stylus type profilometer, Talysurf (Taylor Hobson, Surtronic 3+) as shown in Figure 3.5. The roughness measuring
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conditions are shown in Table 3.3. Roughness measurements were carried out in the transverse direction. The measured profile was digitized and processed through the dedicated advanced surface finish analysis software Talyprofile for evaluation of the roughness parameters. Roughness is defined as the arithmetic value of the profile from the centreline along the length and can be express as
) x ( d ) x ( y L 1 Ra (3.1)
where L is the sampling length, y is the profile curve and x is the profile direction. The average ‟Ra‟ is measured within L = 0.8 mm.
Figure 3.5. Talysurf
Table 3.3. Roughness measuring conditions
Condition Value
Probe tip radius 0.005 mm
Measuring range 0.800 mm
Traverse length 4.000 mm
Speed 1.000 mm/s
Filter 2 CR
3.6.3.Microscope
The photo graphs of the machined parts were taken by microscope (RADIAL INS-TRUMENT) with Samsung camera setup (45X magnification) Figure 3.6.
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. Figure 3.6. Microscope with camera attachment 3.6.4.Scanning electron microscope
The surfaces of the specimens are examined directly by scanning electron microscope (SEM) JEOL JSM-6480LV as shown in Figure 3.7. The JEOL JSM-6480LV is a high-performance, scanning electron microscope with 1000 magnification. The low vacuum (LV) mode (which can be accessed by the click of a mouse), allows for observation of specimens which cannot be viewed at high vacuum due to excessive water content or due to a non-conductive surface. Its asynchronous five-axis stage can accommodate a specimen of up to 8-inches in diameter.
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3.7. Experimental design
A commonly use approach in scientific and engineering investigation is to study one factor at a time or study several factors one at a time. This approach has inherent disadvantages like, more experimental runs are require for the precision in effect estimation, factor interaction effects cannot be studied, conclusions are not general and may miss the optimal settings of factor. To overcome this problem design of experiment (DOE) is a scientific approach to effectively plan and perform experiments, using statistics and are commonly used to improve the quality of a products or processes. Such methods enable the user to define and study the effect of every single condition possible in an experiment where numerous factors are involved [69, 70]. EDM is such a process in which a number of control factors collectively determine the performance output in other words the part quality and productivity. Hence, in the present work a statistical technique called response surface methodology is used to optimize the process parameters leading to the improvement in performance output of the part under study. The most important stage in the DOE lies in the selection of the control factors and their levels. EDM process has large number of process related parameters which are defined in Table 3.4.
Based on initial trials and exhaustive literature review [71] four parameters namely, discharge current (Ip), pulse-on-time (Ton), duty factor (τ) and flushing pressure (Fp) are identified as significant factors and hence are selected to study their influence on output responses as material removal rate (MRR), tool wear rate (TWR), surface roughness (Ra) and circularity (r1/r2). The levels of factors are selected in accordance with the permissible minimum
and maximum settings recommended by the equipment manufacturer, experience, and real industrial applications. The operating conditions under which tests are carried out are given in Table 3.5.
Table 3.4. Process parameters in EDM
Process parameter Definition
Spark On-time (pulse time or Ton)
The duration of time (μs) the current is allowed to flow per cycle. Material removal is directly proportional to the amount of energy applied during this pulse-on-time. This energy is really controlled by the peak current and the length of the pulse-on-time.
Spark Off-time (pause time or Toff )
The duration of time (μs) between the sparks (that is to say, pulse-on-time). This time allows the molten material to solidify and to be wash out of the arc gap. This
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parameter is to affect the speed and the stability of the cut. Thus, if the off-time is too short, it will cause sparks to be unstable.
Arc gap (or gap)
The Arc gap is distance between the electrode and work piece during the process of EDM. It may be called as spark gap. Spark gap can be maintained by servo system.
Discharge current (Ip)
Current is measured in amp Allowed to per cycle. Spark energy is directly controlled by discharge current which leads to the Material removal rate.
Duty factor (τ)
Duty factor is the pulse-on-time relative to the total cycle time (Ton+Toff) and expressed in percentage. It refers to the stability of spark.
The open circuit voltage - V
o
V
o is the potential that can be measure by volt meter when
there is no spark between electrodes. The working voltage - V
w Vw is the potential exerted during machining.
Polarity
There are two type of polarity according to the connectivity of work piece. If work piece is connected to anode then it is positive (+ve) polarity and if connected to cathode, it is negative (-ve) polarity. Positive polarity is significant to MRR and negative polarity is significant to surface roughness.
Flushing
Flushing is necessary to carry out the eroded material from work piece to avoid deposition.
Dielectric medium
Since EDM is spark erosion process a medium is necessary. Initially the medium is ionised and plasma channel is created which leads to spark.
Table 3.5. Factors and their levels
Parameters Symbols Level Codes
-1 0 1
Discharge current (Ip) in A A 3 5 7
Pulse on time (Ton) in µs B 100 200 300
Duty Factor (τ) in % C 80 85 90
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3.7.1.Response surface experimental design
Response surface methodology (RSM) is a collection of statistical and mathematical technique useful for developing, improving and optimizing process. It deals with the situation where several input variable potentially influence the performance measure or quality of the product or process. The performance measure or quality is known as response. Response surface methodology (RSM) quantifies the relationship between the controllable input parameters and the obtained response. The goal is to find a suitable approximation for the true functional relationship between independent variables and the response. Usually a second-order model as given in Eq. 3.2 is utilized in response surface methodology.
ε x x β x β x β β Y
∑
∑
∑ ∑
j i ij i j k 1 i 2 i ii i k 1 i i 0 (3.2)where Y is the corresponding response of input variables Xi, Xi2 and XiXj are the square and
interaction terms of parameters respectively. β0, βi, βii and βij are the unknown regression
coefficients and ε is the error.
A full factorial design would provide estimation of all the required regression parameters (β). However, full factorial designs are expensive to use as the number of runs increases rapidly with the number of factors. Therefore, for the purpose of analysis Box-Behnken design is useful as it help to fit the second order model to the response with the use of a minimum number of runs [69, 70]. Box-Behnken design performs non-sequential experiments. That is, only planning to perform the experiment once. These designs allow efficient estimation of the first- and second-order coefficients. Because Box-Behnken designs have fewer design points, they are less expensive to run than central composite designs with the same number of factors.
Box-Behnken designs can also prove useful in the safe operating zone for the process. Central composite designs usually have axial points outside the "cube" (unless it is specified less than or equal to one). These points may not be in the region of interest, or may be impossible to run because they are beyond safe operating limits. Box-Behnken designs do not have axial points, thus, it can be sure that all design points fall within the safe operating zone. Box-Behnken designs also ensure that all factors are never set at their high levels simultaneously. In practice, two or three centre runs are sufficient. In order to get a reasonable estimate of experimental error, three centre runs are chosen in the present work. Twenty seven base runs including three centre points are generated in MINITAB 15 as shown in Table 3.6.
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Table 3.6. Experimental plan for Box-Behnken design
Run Order Ip(A) Ton(B) τ(C) Fp(D)
1 0 -1 0 1 2 0 0 1 -1 3 -1 0 1 0 4 1 0 0 -1 5 0 0 0 0 6 0 0 0 0 7 0 0 -1 1 8 -1 0 0 1 9 -1 -1 0 0 10 0 -1 1 0 11 1 1 0 0 12 1 -1 0 0 13 0 1 0 1 14 0 0 -1 -1 15 0 1 1 0 16 0 1 0 -1 17 0 0 1 1 18 1 0 -1 0 19 0 -1 0 -1 20 0 -1 -1 0 21 0 1 -1 0 22 1 0 0 1 23 -1 1 0 0 24 -1 0 -1 0 25 -1 0 0 -1 26 0 0 0 0 27 1 0 1 0 3.8. Data collection
Four controllable parameters such as discharge current (Ip), pulse-on-time (Ton), duty factor (τ) and flushing pressure (Fp) are considered in this study. The experimental design is made as per Box-Behnken design of response surface methodology because it is capable of generating a satisfactory prediction model with few experimental runs [72, 73]. In three level four factor experimental design, the total number of experimental runs is twenty seven having three center points. To run the experiment smoothly the parametric levels are decoded using the Eq. 3.3.
(3.3) 2 X -X 2 X X -X = (Z) Value Coded min max min max
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where Z is coded value (-1, 0, 1), Xmax and Xmin is maximum and minimum value of actual
variable and X is the actual value of corresponding variable.
The weight of tool and work piece is taken and positioned at two electrodes. Each experiment is carried out for one hour and final weight of tool and work piece is measured. The initial weight and final weight for different experiment along with surface roughness are listed in Table 3.7 and Table 3.8. Table 3.7 and Table 3.8 shows experimental table for brass and copper tool, AISI D2 steel tool work piece combination respectively.
Table 3.7. Experiment table for brass AISI D 2 steel combination
Expt. No. Ip (A) Ton (µs) τ (%) Fp (bar) Initial Wt. (Job) Final Wt. (Job) Initial Wt. (Tool) Final Wt. (Tool) Ra 1 3 100 85 0.3 244.261 243.534 213.45 212.503 3.93 2 7 100 85 0.3 243.534 241.976 212.503 210.712 4.57 3 3 300 85 0.3 241.976 241.229 210.597 209.955 4.65 4 7 300 85 0.3 239.166 235.915 208.967 207.289 7.59 5 5 200 80 0.2 245.607 244.261 214.428 213.45 6.52 6 5 200 90 0.2 215.439 213.562 200.44 198.822 6.15 7 5 200 80 0.4 213.562 212.209 188.685 187.624 6.4 8 5 200 90 0.4 208.646 206.72 177.531 175.858 5.93 9 3 200 80 0.3 239.928 239.207 207.284 206.614 5.17 10 7 200 80 0.3 239.207 236.76 206.614 205.166 6.47 11 3 200 90 0.3 236.76 235.801 205.166 204.188 4.55 12 7 200 90 0.3 235.801 232.924 204.188 201.853 5.48 13 5 100 85 0.2 232.924 231.734 201.853 200.44 5.49 14 5 300 85 0.2 231.732 230.023 195.305 194.178 7.35 15 5 100 85 0.4 230.02 228.851 194.178 192.749 5.07 16 5 300 85 0.4 228.851 227.145 192.749 191.599 7.46 17 3 200 85 0.2 249.21 248.337 217.197 216.378 5.27 18 7 200 85 0.2 248.337 245.607 216.378 214.428 7.73 19 3 200 85 0.4 227.145 226.278 191.599 190.736 4.69 20 7 200 85 0.4 226.278 223.508 190.736 188.683 6.83 21 5 100 80 0.3 212.209 211.276 187.624 186.586 4.28 22 5 300 80 0.3 211.276 209.86 180.026 179.152 8.51 23 5 100 90 0.3 209.86 208.648 179.152 177.532 4.47 24 5 300 90 0.3 206.72 204.757 175.858 174.475 7.79 25 5 200 85 0.3 204.757 203.072 174.475 173.083 6.21 26 5 200 85 0.3 203.072 201.417 173.083 171.636 5.77 27 5 200 85 0.3 201.417 199.777 171.636 170.219 5.8
